Find and sketch the response of a dynamic system described by the equation

\[6 \dot{y}+y=f(t),\]

with the initial condition \(y(0)=4\) when the input is:

(a) \(f(t)=10\)

(b) \(f(t)=5 e^{-\frac{t}{2}}\)

(c) \(f(t)=10+5 e^{-\frac{t}{2}}\)

(d) \(f(t)=\sin t+\cos t\)